Influence of local strain heterogeneity on high piezoelectricity in $0.5\mathrm{Ba}\left(\mathrm{Z}{\mathrm{r}}_{0.2}\mathrm{T}{\mathrm{i}}_{0.8}\right){\mathrm{O}}_3-0.5\left(\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\right)\mathrm{Ti}{\mathrm{O}}_3$ ceramics

Dielectric and mechanical spectroscopies have been used to investigate ferroelectric transitions and twin wall dynamics in the lead-free ceramic $0.5\mathrm{Ba}\left(\mathrm{Z}{\mathrm{r}}_{0.2}\mathrm{T}{\mathrm{i}}_{0.8}\right){\mathrm{O}}_3-0.5\left(\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\right)\mathrm{Ti}{\mathrm{O}}_3$ (abbreviated as BZT-50BCT), which is known to have a high piezoelectric coefficient ($d_{33}>545\mathrm{pC}/\mathrm{N}$). Results from dynamical mechanical analysis in the frequency range 0.2–20 Hz and resonant ultrasound spectroscopy in the frequency range $\sim 0.1–1.2\mathrm{MHz}$ confirm the existence of three phase transitions with falling temperature, at $\sim 360\mathrm{K}$ (cubic-tetragonal), $\sim 304\mathrm{K}$ (tetragonal-orthorhombic), and $\sim 273\mathrm{K}$ (orthorhombic-rhombohedral). In comparison with $\mathrm{BaTi}{\mathrm{O}}_3$, however, the transitions are marked by rounded rather than sharp minima in the shear modulus. The pattern of acoustic loss is also quite different from that shown by $\mathrm{BaTi}{\mathrm{O}}_3$ in having a broad interval of high loss at low temperatures, consistent with a spectrum of relaxation times for interactions of ferroelastic twin walls. Differences in the dielectric properties also suggest more relaxor like characteristics for BZT-50BCT. It is proposed that the overall pattern of behavior is significantly influenced by strain heterogeneity at a local length scale in the perovskite structure due to the substitution of cations with different ionic radii. The existence of this strain heterogeneity and its influence on the elastic behavior near the transition points could be contributory factors to the development of adaptive nanoscale microstructures and enhanced piezoelectric properties.

Figure 1

XRD profiles of BTO (black) and BZT-50BCT (red) measured at ambient temperature $\left(25{}^{\circ }\mathrm{C}\right)$, indicating that homogeneous single phase perovskites were obtained by the conventional fabrication process. Also given are the refined lattice parameters.

Figure 2

SEM images of (a) BTO and (b) BZT-50BCT ceramics, indicating the different grain size between BZT-50BCT and BTO samples.

Figure 3

(a) Phase diagram of BZT-$x\mathrm{BCT}$ system for $x=20–60$ and (b) connection from BZT-50BCT to $\mathrm{BaTi}{\mathrm{O}}_3$, as determined from dielectric permittivity measurements. The C/T/intermediate phase/R phase regions of BZT-50BCT can be smoothly connected with the C/T/O/R phase regions of pure BTO, indicative of orthorhombic symmetry for the intermediate phase of BZT-50BCT [12]. (c) Permittivity for BZT-50BCT, measured in the frequency range $0.06–100\mathrm{kHz}$. The highest value for the piezoelectric coefficient, $d_{33}=545\mathrm{pC}/\mathrm{N}$ occurs at the T-O transition point $(\sim 304\mathrm{K})$.

Figure 4

(a) Stack of RUS spectra for BTO ceramic collected in the range 5–500 K. (b) Stack of RUS spectra for BZT-50BCT ceramic collected in the range 5–540 K. The $y$ axis is the amplitude of the RUS signal, but each spectrum has been displaced in proportion to the temperature at which it was collected, and the right arrows point to high temperature ($T$) from low temperature. Weak resonance peaks above 300 K, which are independent of temperature, are from the alumina buffer rods. Similar weak peaks below 300 K, which are also independent of temperature, come from some part of the low temperature holder. Temperature evolution of the squared frequency ($f^2$, black markers, left axis) and inverse mechanical quality factor ($Q^{-1}$, red or purple markers, right axis) of (c) BTO and (d) BZT-50BCT. Minima in $f^2$ correspond to known phase transitions. A Debye loss peak appears at $\sim 70\mathrm{K}$ in BTO and is replaced by a wide temperature interval of high loss in BZT-50BCT.

Figure 5

DMA data for BZT-50BCT in the frequency range 0.2–20 Hz: (a) Temperature dependence of the storage modulus. (b) Temperature dependence of loss, $tan\delta$. Three minima in the storage modulus coincide with maxima or a shoulder in $tan\delta$ at $\sim 360\mathrm{K}$ (C-T transition), $\sim 304\mathrm{K}$ (T-O transition), $\sim 273\mathrm{K}$, (T-O transition).

Figure 6

Comparison of results from dielectric spectroscopy and RUS for BTO: (a) Permittivity (${\varepsilon }_{\mathrm{r}}$, multicolor markers, left $y$ axis) and elastic compliance ($1/f^2$, black markers, right $y$ axis), (b) dielectric loss ($tan\delta$, multicolor marker, left $y$ axis) and acoustic loss ($Q^{-1}$, black markers, right $y$ axis). Dielectric data were collected during continuous cooling. There are clear and discrete anomalies associated with each of the three phase transitions. An additional dielectric loss peak occurs in the stability field of the orthorhombic structure but differs from the others in being strongly dependent on frequency.

Figure 7

Comparison of dielectric spectroscopy and mechanical spectroscopy data for BZT-50BCT: (a) Dielectric permittivity (measured at $\sim 10–{10}^5\mathrm{Hz}$), elastic compliance from DMA (inverse of storage modulus, measured at $\sim {10}^0–{10}^1\mathrm{Hz}$), and elastic compliance from RUS ($1/f^2$, measured at $\sim {10}^5–{10}^6\mathrm{Hz}$). (b) Dielectric loss and acoustic loss. DMA data were collected during continuous heating, dielectric data during continuous cooling. The elastic compliance data still show clear anomalies associated with the phase transitions, but the permittivity has a peak only at $T_c$. The patterns of dielectric and acoustic loss differ markedly from each other and from those seen in BTO under the same experimental conditions.

Figure 8

The temperature evolution of $f^2$ (proportional to shear elastic modulus) in the temperature range of 360–730 K for the BZT-50BCT and BTO polycrystalline ceramics. The Burns temperature ($T_{\mathrm{B}}$) is defined as the preliminary softening of PNRs. The $T_{\mathrm{B}}$ of BZT-50BCT (544 K) is clearly higher than that of the BTO case (510 K). This may be due to the strain heterogeneity state of BZT-50BCT.